Finite difference stencils based on particle strength exchange schemes for improvement of vortex methods

Philippe Poncet (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

The method of Particle Strength Exchange aims at solving the viscous part of the Navier-Stokes equations, when split into diffusive and corrective parts. We present their formulation in the context of vortex methods. The present work follows the classical analysis by Degond and MasGallic whose formulas were obtained by means of integration of continuous functions. It shows that one gets different operators when integration is discrete, and leads to a substantial gain of accuracy. This scheme is then applied to several three-dimensional flows to exhibit convergence rate and impact on conservation laws at moderate Reynolds numbers. A sensitivity analysis is finally provided in order to carry out the good behavior of these schemes in both Eulerian and Lagrangian contexts.

Domaines: Mathématiques [math]; Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Philippe Poncet. Finite difference stencils based on particle strength exchange schemes for improvement of vortex methods. Journal of Turbulence, 2006, 7, pp.N23. ⟨10.1080/14685240600595586⟩. ⟨hal-02010666⟩